What is grade 1 “thinking math”? Should your child learn it, common problem types and how to teach it at home
Grade 1 “thinking math” (what Vietnamese parents call “toan tu duy”) is the phrase parents search for most when their child starts primary school – yet every center uses the name for something different. Here: what it is, the 6 problem types, whether your child should learn it, and how to teach it at home in 15 minutes a day.
Learning math by understanding and thinking, not only getting sums right by following a model.
- Quantities, splitting and combining, patterns, comparing, reasoning
- Supports school math; does not replace it
- Start once your child counts and recognizes numbers comfortably
- 10–15 minutes a day, through games and worksheets at the right level
- The soroban’s strength: mental math and place value
- Logic and geometry: need other problems and games
What is grade 1 thinking math? How is it different from school math?
In Vietnam, “thinking math” is a common name for many ways of teaching math outside the textbook, not one fixed program: Singapore-style logic math, soroban, Finger Math, franchised abacus programs, Kumon… What they share is a focus on how the child thinks: why 7 + 5 = 12, what comes after 2, 4, 6, which shape is the odd one out.
| Grade 1 math at school | Grade 1 thinking math | |
|---|---|---|
| Goal | Standard knowledge: numbers to 100, addition and subtraction without carrying, shapes, measurement, telling the time | Understanding what numbers really are, ways of thinking, the habit of working things out |
| Problem types | Following the model in the textbook, skill practice | Missing numbers, comparing, patterns, reasoning, putting shapes together, mental math |
| How children learn | The teacher explains – the whole class works | Games, hands-on materials (beads, cards, the abacus), questions and discussion, open problems |
| Assessment | Right/wrong, scores | How the child works it out, progress compared with themselves |
The two are not opposites: Vietnam’s 2018 general education curriculum also stresses “mathematical thinking and reasoning” from grade 1. Thinking math simply does it more thoroughly, with time and materials a class of 40 pupils rarely has.
6 common types of grade 1 thinking math problems (with examples)
1. Recognizing quantities and how numbers are made
Example: look at 7 dots (a row of 5 and a row of 2) and say “seven” without counting; “7 is 5 and how many?”; “How many tens and ones make 12?”. This is the foundation for every other type.
Each number has exactly one shape on the soroban (7 = one 5-bead + two 1-beads), so soroban children become very secure at this type. See the numbers 0–9 on What is a soroban?.
2. Missing numbers
Example: 3 + ☐ = 7; ☐ − 2 = 5; 6 = 4 + ☐. Children see a sum as a relationship (“3 plus what makes 7?”) – a stepping stone to the subtraction 7 − 3.
3. Comparing and writing >, <, =
Example: 7 + 2 ○ 10; 2 + 6 ○ 3 + 5; 15 ○ 9 + 6. Work out both sides, then compare – two steps in one problem.
A common mistake: comparing straight away using the first number they see.
4. Finding patterns
Example: 2, 4, 6, __, __; 20, 18, 16, __; circle – square – circle – square – __. Closest to “thinking” – and children’s favorite once they can do it.
5. Reasoning and word problems
Example: “An has 5 candies and gives Binh 2. How many does An have left?”; “3 children, 2 cakes each – how many cakes?” (counting in twos); “Minh is taller than Lan, and Lan is taller than Ha. Who is the shortest?”. The child reads (or listens), pictures the situation, and only then chooses the operation.
6. Shapes and space
Example: two triangles make a square; count the triangles in a large figure; find the odd shape out; imagine a shape seen from above. This trains spatial imagination – the ability used to picture an abacus in the head.
Most programs also include mental math (within 10, 20, then 100) – slow calculation holds a child back in every type. See How to teach a grade 1 child fast mental math.
Should your child learn grade 1 thinking math?
Yes, if the three conditions below are met – no, if any one of them is missing.
It is not “getting ahead of the curriculum”; without that foundation, play counting games for a few more weeks.
A 6-year-old is at school all day; 2 more hours in the evening can easily make a child hate math.
Kodomo Soroban Center’s standard: 80% correct within the set time means moving on. Too easy is boring; too hard is frightening.
Benefits you can see after 2–3 months:
- Your child counts on their fingers less
- They can explain how they worked it out
- They enjoy setting “puzzles” for their parents
- School math becomes easy
What thinking math cannot do:
- Turn a child into a “prodigy” after one course
- Replace reading, writing and physical activity
Still deciding? Soroban or Finger Math? compares 4 popular approaches.
Where to learn grade 1 thinking math: at home, online or in a class?
| At home with parents | Online (apps, videos) | In a class | |
|---|---|---|---|
| Suits you when | Parents have 15 minutes a day and patience; the child is happy to sit with them | Extra practice after understanding; the child is self-motivated | You need someone to teach the right technique (especially mental math and soroban), and the child needs classmates and the rhythm of a class |
| Strengths | Cheap, flexible, brings you closer | Lots of problems, instant feedback | The teacher spots mistakes; study habits; regularity |
| Weaknesses | Parents lose patience easily; hard to see where the child goes wrong | Screens; the child “taps to get it over with” | Travel time; you need to choose the class carefully |
The best combination we see in our students’ families:
Online only for mental math practice, such as our Flash Anzan tool.
How many children? Which curriculum? What do children do with their hands? What do parents get to use at home? Is learning soroban good for children? has 6 questions to take to a trial lesson.
How to teach grade 1 thinking math at home: 15 minutes a day
- 3 minutes: warm up with quantities.
Hold up fingers, dot cards or beans in rows of 5 – your child says the number straight away, then “7 is 5 and how many?”.
- 7 minutes: one problem type, one week.
This week missing numbers, next week comparing, then patterns; 8–10 problems a day, gently timed. Repeat for 5 days: “knowing” becomes “doing it without thinking”.
- 3 minutes: one open “puzzle”.
“How many ways to make 10 from two numbers?”, “6 sticks into 2 triangles?”. There is no single answer – your child talks, you listen.
- 2 minutes: the child checks and records their work.
Your child marks right and wrong with the answer page and writes down the time. Seeing their own progress is the biggest motivation.
The golden rule: ask “What do you think?” and “How do you know?” instead of explaining for five minutes.
Where does the soroban fit in “grade 1 thinking math”?
We are a soroban center, so let us be clear about the boundaries.
What the soroban does very well
- How numbers are made, place value (each rod is one place)
- Splitting and combining with 5 and 10 (the 5-friend and 10-friend rules)
- Mental math (the abacus in the head)
- Concentration and the habit of sitting down to study
What the soroban does not teach
- Reasoning in word problems
- Geometry
- Shape patterns
That is why in our classes, every lesson includes “grid calculation” and number games alongside the abacus; at home, add thinking math worksheets (types 2–6). See the level pathway for each module.
Grade 1 thinking math worksheets (PDF with answers)
The free worksheets are on the Free worksheets page; each is 2 A4 pages: problems and answers.
- Worksheet 19: missing numbers
- Worksheet 20: comparing with > < =
- Worksheet 21: number patterns
- Worksheet 22: 100-square grid calculation – subtraction
- Worksheets 13–18: mental math within 10 – 20 – 100
Frequently asked questions
What is grade 1 thinking math?
It is a way of learning math that focuses on understanding and thinking: recognizing quantities, splitting and combining numbers, filling in missing numbers, comparing, finding patterns, and reasoning from situations and pictures. Thinking math supports school math; it does not replace it.
How is thinking math different from ordinary math?
School math focuses on standard knowledge and skills that follow a model; thinking math focuses on how the child thinks and works things out, through games, hands-on materials and open problems. Each needs the other: understanding the basics helps children do their schoolwork faster and more securely.
At what age should children start thinking math?
Once your child counts confidently and recognizes numbers to 20 – usually at 5–6 years old. Before that, counting and number games are enough. For soroban, Kodomo Soroban Center accepts children from 5 years old.
Is grade 1 thinking math good for children, and can it do any harm?
It is good when the level is right (about 80% correct), the time is reasonable (10–15 minutes a day or 1 class a week) and there are games. It does harm when children are pushed to do too much, the problems are too hard, or it is only exam drilling – the child will become afraid of math.
Where can I find grade 1 thinking math worksheets?
The Free worksheets page of Kodomo Soroban Center has 10 worksheets for grades 1–2 (mental math within 10, 20 and 100; missing numbers; comparing; patterns; grid calculation), each with answers, to print at home.
Try a free soroban lesson
Classes of 3–5 children at Vinhomes Gardenia (Hanoi), 70 minutes each, taught exactly as in Japan. Phone · Zalo 096.802.8484.
Written by the teaching team of Kodomo Soroban Center, following the method and textbooks of Kodomo School (Japan, teaching soroban since 1976). The center is licensed by the Hanoi Department of Education and Training, and our project is a 2026 EDU-Port Nippon supported project of Japan’s Ministry of Education (MEXT).
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